{
  "version": 1,
  "topic": "TH06",
  "title": "PT PH and PS flash specifications explained",
  "createdAt": "2026-10-24",
  "case": {
    "title": "Peng-Robinson Heat-Duty and Isenthalpic Flash Calculator",
    "premise": "Fixed controls: Inlet absolute pressure = 5 MPa(a); Inlet equilibrium temperature = 330 K; Outlet absolute pressure = 1 MPa(a); Methane feed mole fraction = 0.5 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.05 dimensionless.",
    "formula": "Internal SI: hbar_out(p_out,T_out,z)=hbar_in(p_in,T_in,z)+q(J/kg)*Mz(kg/mol). Solve F(T)=hbar_out-hbar_in-q*Mz=0 over 180-450 K. UI q(kJ/kg) is multiplied by 1000. q=0 is isenthalpic, not isothermal.; PR phase enthalpy is ideal-gas component enthalpy plus cubic residual enthalpy. The bulk molar enthalpy equals (1-beta)*hL+beta*hV. Native ideal-gas functions are pinned with the component data; no constant-Cp or vapor-only latent-heat shortcut is used. Compare enthalpy differences on the same fixed reference.; At common T and p, xi*phiL_i=yi*phiV_i. zi=(1-beta)*xi+beta*yi; Ki=yi/xi and sum[zi*(Ki-1)/(1+beta*(Ki-1))]=0. CoolProp performs stability analysis and phase-split iteration; Wilson K-factors are initial guesses, not the final equilibrium solution.",
    "variables": "Specific heat input (positive into fluid) is varied within the supported input range. C1-C6 only with normal C4-C6, zero binary interaction parameters, no volume translation and the pinned ideal-gas caloric functions. No C7+ heat-capacity assumption, wet/sour gas, arbitrary mixture, chemical reaction, multiple liquids or solid phase. Agreement with an independent implementation does not replace measured-PVT validation.",
    "steps": [
      {
        "label": "Define the baseline",
        "calculation": "Specific heat input (positive into fluid) (kJ/kg) = 0",
        "explanation": "Fixed controls: Inlet absolute pressure = 5 MPa(a); Inlet equilibrium temperature = 330 K; Outlet absolute pressure = 1 MPa(a); Methane feed mole fraction = 0.5 dimensionless; Ethane feed mole fraction = 0.15 dimensionless; Propane feed mole fraction = 0.15 dimensionless; n-Butane feed mole fraction = 0.1 dimensionless; n-Pentane feed mole fraction = 0.05 dimensionless; n-Hexane feed mole fraction = 0.05 dimensionless."
      },
      {
        "label": "Select the relation",
        "calculation": "Internal SI: hbar_out(p_out,T_out,z)=hbar_in(p_in,T_in,z)+q(J/kg)*Mz(kg/mol). Solve F(T)=hbar_out-hbar_in-q*Mz=0 over 180-450 K. UI q(kJ/kg) is multiplied by 1000. q=0 is isenthalpic, not isothermal.; PR phase enthalpy is ideal-gas component enthalpy plus cubic residual enthalpy. The bulk molar enthalpy equals (1-beta)*hL+beta*hV. Native ideal-gas functions are pinned with the component data; no constant-Cp or vapor-only latent-heat shortcut is used. Compare enthalpy differences on the same fixed reference.; At common T and p, xi*phiL_i=yi*phiV_i. zi=(1-beta)*xi+beta*yi; Ki=yi/xi and sum[zi*(Ki-1)/(1+beta*(Ki-1))]=0. CoolProp performs stability analysis and phase-split iteration; Wilson K-factors are initial guesses, not the final equilibrium solution.",
        "explanation": "Specific heat input (positive into fluid) is varied within the supported input range. C1-C6 only with normal C4-C6, zero binary interaction parameters, no volume translation and the pinned ideal-gas caloric functions. No C7+ heat-capacity assumption, wet/sour gas, arbitrary mixture, chemical reaction, multiple liquids or solid phase. Agreement with an independent implementation does not replace measured-PVT validation."
      },
      {
        "label": "Substitute the values",
        "calculation": "q = 0 kJ/kg; with the fixed controls above, the workflow evaluates Outlet equilibrium temperature = 296.256406 K; Temperature change = -33.7435936 K difference",
        "explanation": "Retain intermediate precision. The displayed values are rounded only after evaluation."
      },
      {
        "label": "Read the result",
        "calculation": "Outlet equilibrium temperature (K) = 296.256406; Temperature change (K difference) = -33.7435936",
        "explanation": "Both pressures must be 0.1-10 MPa(a), outlet<=inlet; inlet and every trial/outlet temperature must remain 180-450 K. q is restricted to -500 to 500 kJ/kg and must admit an energy root in that temperature envelope. The existing endpoint near-critical/vanishing-phase and closure gates still apply. No shaft/compression work, kinetic or potential-energy changes, frictional pressure traverse or critical-flow prediction. Steady instantaneous vapor-liquid equilibrium with prescribed pressure and specific heat, not a coupled well heat-transfer model, PH property API with an arbitrary external enthalpy reference, separator sizing, residence time or transient simulation. The outer bounded energy root is this application's wrapper around native PT flashes, not a claim of native general mixture PH support. Failure to bracket a root is reported, never extrapolated or clipped."
      }
    ],
    "result": "Outlet equilibrium temperature (K) = 296.256406; Temperature change (K difference) = -33.7435936",
    "interpretation": "Both pressures must be 0.1-10 MPa(a), outlet<=inlet; inlet and every trial/outlet temperature must remain 180-450 K. q is restricted to -500 to 500 kJ/kg and must admit an energy root in that temperature envelope. The existing endpoint near-critical/vanishing-phase and closure gates still apply. No shaft/compression work, kinetic or potential-energy changes, frictional pressure traverse or critical-flow prediction. Steady instantaneous vapor-liquid equilibrium with prescribed pressure and specific heat, not a coupled well heat-transfer model, PH property API with an arbitrary external enthalpy reference, separator sizing, residence time or transient simulation. The outer bounded energy root is this application's wrapper around native PT flashes, not a claim of native general mixture PH support. Failure to bracket a root is reported, never extrapolated or clipped.",
    "control": "Specific heat input (positive into fluid) (kJ/kg)",
    "columns": [
      "Specific heat input (positive into fluid) (kJ/kg)",
      "Outlet equilibrium temperature (K)",
      "Temperature change (K difference)"
    ],
    "rows": [
      [
        -10,
        294.0786140485943,
        -35.92138595140568
      ],
      [
        -5,
        295.1688010747239,
        -34.83119892527611
      ],
      [
        0,
        296.2564064340768,
        -33.74359356592322
      ],
      [
        5,
        297.34141746539535,
        -32.65858253460465
      ],
      [
        10,
        298.42380852987844,
        -31.576191470121557
      ]
    ],
    "baseline": 2,
    "rowNotes": [
      "Specific heat input (positive into fluid) (kJ/kg) = -10. Outlet equilibrium temperature (K): 294.078614; Temperature change (K difference): -35.921386.",
      "Specific heat input (positive into fluid) (kJ/kg) = -5. Outlet equilibrium temperature (K): 295.168801; Temperature change (K difference): -34.8311989.",
      "Specific heat input (positive into fluid) (kJ/kg) = 0. Outlet equilibrium temperature (K): 296.256406; Temperature change (K difference): -33.7435936.",
      "Specific heat input (positive into fluid) (kJ/kg) = 5. Outlet equilibrium temperature (K): 297.341417; Temperature change (K difference): -32.6585825.",
      "Specific heat input (positive into fluid) (kJ/kg) = 10. Outlet equilibrium temperature (K): 298.423809; Temperature change (K difference): -31.5761915."
    ],
    "provenance": "Original recorded synthetic cases solved with the site's peng-robinson-energy-flash engine. The full inputs, outputs and diagnostic rows are in the downloadable JSON. These are discrete solved states; the lesson does not interpolate a new solve.",
    "questions": [
      {
        "question": "Reproduce the baseline Outlet equilibrium temperature (K) without rounding intermediate values.",
        "answer": "q = 0 kJ/kg; with the fixed controls above, the workflow evaluates Outlet equilibrium temperature = 296.256406 K; Temperature change = -33.7435936 K difference. Outlet equilibrium temperature (K) = 296.256406. Both pressures must be 0.1-10 MPa(a), outlet<=inlet; inlet and every trial/outlet temperature must remain 180-450 K. q is restricted to -500 to 500 kJ/kg and must admit an energy root in that temperature envelope. The existing endpoint near-critical/vanishing-phase and closure gates still apply. No shaft/compression work, kinetic or potential-energy changes, frictional pressure traverse or critical-flow prediction. Steady instantaneous vapor-liquid equilibrium with prescribed pressure and specific heat, not a coupled well heat-transfer model, PH property API with an arbitrary external enthalpy reference, separator sizing, residence time or transient simulation. The outer bounded energy root is this application's wrapper around native PT flashes, not a claim of native general mixture PH support. Failure to bracket a root is reported, never extrapolated or clipped."
      },
      {
        "question": "Compare the first and last recorded scenarios. Which input changes?",
        "answer": "Specific heat input (positive into fluid) (kJ/kg) changes from -10 to 10. Other controls remain as stated in the premise. Outlet equilibrium temperature (K) changes from 294.078614 to 298.423809."
      },
      {
        "question": "What would be needed to apply this example to a different physical system?",
        "answer": "Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. Specific heat input (positive into fluid) is varied within the supported input range. C1-C6 only with normal C4-C6, zero binary interaction parameters, no volume translation and the pinned ideal-gas caloric functions. No C7+ heat-capacity assumption, wet/sour gas, arbitrary mixture, chemical reaction, multiple liquids or solid phase. Agreement with an independent implementation does not replace measured-PVT validation. Both pressures must be 0.1-10 MPa(a), outlet<=inlet; inlet and every trial/outlet temperature must remain 180-450 K. q is restricted to -500 to 500 kJ/kg and must admit an energy root in that temperature envelope. The existing endpoint near-critical/vanishing-phase and closure gates still apply. No shaft/compression work, kinetic or potential-energy changes, frictional pressure traverse or critical-flow prediction. Steady instantaneous vapor-liquid equilibrium with prescribed pressure and specific heat, not a coupled well heat-transfer model, PH property API with an arbitrary external enthalpy reference, separator sizing, residence time or transient simulation. The outer bounded energy root is this application's wrapper around native PT flashes, not a claim of native general mixture PH support. Failure to bracket a root is reported, never extrapolated or clipped."
      }
    ]
  },
  "recorded": {
    "kind": "workflow",
    "workflow": "peng-robinson-energy-flash",
    "parameter": "q",
    "runs": [
      {
        "inputs": {
          "p_in": 5,
          "T_in": 330,
          "p_out": 1,
          "q": -10,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "Steady C1-C6 heat-duty flash: h_out=h_in+q, with q positive into the fluid. q=0 is isenthalpic throttling, not an isothermal pressure drop. Zero kij; no shaft work, kinetic/potential energy, heat-transfer rate closure or C7+ caloric approximation.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Outlet equilibrium temperature",
              "value": 294.0786140485943,
              "unit": "K"
            },
            {
              "label": "Temperature change",
              "value": -35.92138595140568,
              "unit": "K difference"
            },
            {
              "label": "Prescribed specific heat input",
              "value": -10,
              "unit": "kJ/kg"
            },
            {
              "label": "Absolute molar energy residual",
              "value": 1.249554770765826e-7,
              "unit": "J/mol"
            },
            {
              "label": "Outlet caloric PT evaluations",
              "value": 66,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 17.1569595788289,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.8313322774150023,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.676642332136788,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 615.4674888346758,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 11.714721844215305,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 3.469446951953614e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 6.060887486336597e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 1.95057303642443e-11,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
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          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
              {
                "name": "Feed",
                "x": [
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                  3,
                  4,
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                  6
                ],
                "y": [
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                  0.15,
                  0.15,
                  0.1,
                  0.05,
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                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
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                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                "mode": "lines+markers"
              },
              {
                "name": "Vapor",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                ],
                "mode": "lines+markers",
                "line": {
                  "dash": "dash"
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              }
            ]
          }
        }
      },
      {
        "inputs": {
          "p_in": 5,
          "T_in": 330,
          "p_out": 1,
          "q": -5,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "Steady C1-C6 heat-duty flash: h_out=h_in+q, with q positive into the fluid. q=0 is isenthalpic throttling, not an isothermal pressure drop. Zero kij; no shaft work, kinetic/potential energy, heat-transfer rate closure or C7+ caloric approximation.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Outlet equilibrium temperature",
              "value": 295.1688010747239,
              "unit": "K"
            },
            {
              "label": "Temperature change",
              "value": -34.83119892527611,
              "unit": "K difference"
            },
            {
              "label": "Prescribed specific heat input",
              "value": -5,
              "unit": "kJ/kg"
            },
            {
              "label": "Absolute molar energy residual",
              "value": 6.392292561940849e-8,
              "unit": "J/mol"
            },
            {
              "label": "Outlet caloric PT evaluations",
              "value": 66,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 17.00062667550072,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.8361467839148359,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.6845509620356253,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 615.0602173751626,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 11.740160117228385,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 2.0816681711721685e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 5.750828008244113e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 1.9490631331109398e-11,
              "unit": "dimensionless"
            }
          ],
          "rowLabels": [
            "Methane",
            "Ethane",
            "Propane",
            "n-Butane",
            "n-Pentane",
            "n-Hexane"
          ],
          "columns": [
            "Feed z (mol/mol)",
            "Liquid x (mol/mol)",
            "Vapor y (mol/mol)",
            "Liquid allocation (mol/mol feed)",
            "Vapor allocation (mol/mol feed)"
          ],
          "rows": [
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              0.04404433958395035,
              0.005955660416049675
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          ],
          "chart": {
            "xLabel": "Component",
            "yLabel": "Mole fraction",
            "xTicks": {
              "values": [
                1,
                2,
                3,
                4,
                5,
                6
              ],
              "text": [
                "C1",
                "C2",
                "C3",
                "nC4",
                "nC5",
                "nC6"
              ]
            },
            "series": [
              {
                "name": "Feed",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                  0.15,
                  0.15,
                  0.1,
                  0.05,
                  0.05
                ],
                "mode": "lines+markers"
              },
              {
                "name": "Liquid",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                "mode": "lines+markers"
              },
              {
                "name": "Vapor",
                "x": [
                  1,
                  2,
                  3,
                  4,
                  5,
                  6
                ],
                "y": [
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                "mode": "lines+markers",
                "line": {
                  "dash": "dash"
                }
              }
            ]
          }
        }
      },
      {
        "inputs": {
          "p_in": 5,
          "T_in": 330,
          "p_out": 1,
          "q": 0,
          "z1": 0.5,
          "z2": 0.15,
          "z3": 0.15,
          "z4": 0.1,
          "z5": 0.05,
          "z6": 0.05
        },
        "result": {
          "warnings": [
            "Steady C1-C6 heat-duty flash: h_out=h_in+q, with q positive into the fluid. q=0 is isenthalpic throttling, not an isothermal pressure drop. Zero kij; no shaft work, kinetic/potential energy, heat-transfer rate closure or C7+ caloric approximation.",
            "Two-phase equilibrium: beta is vapor moles per feed mole, not vapor mass fraction or in-situ gas holdup. Component allocations in the table are moles per feed mole."
          ],
          "outputs": [
            {
              "label": "Outlet equilibrium temperature",
              "value": 296.2564064340768,
              "unit": "K"
            },
            {
              "label": "Temperature change",
              "value": -33.74359356592322,
              "unit": "K difference"
            },
            {
              "label": "Prescribed specific heat input",
              "value": 0,
              "unit": "kJ/kg"
            },
            {
              "label": "Absolute molar energy residual",
              "value": 1.4498618838842958e-7,
              "unit": "J/mol"
            },
            {
              "label": "Outlet caloric PT evaluations",
              "value": 66,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium phase count",
              "value": 2,
              "unit": "dimensionless"
            },
            {
              "label": "Equilibrium bulk density",
              "value": 16.847014824611545,
              "unit": "kg/m3"
            },
            {
              "label": "Feed molar mass",
              "value": 32.874526,
              "unit": "g/mol"
            },
            {
              "label": "Vapor mole fraction (beta)",
              "value": 0.8409410356828884,
              "unit": "dimensionless"
            },
            {
              "label": "Vapor mass fraction",
              "value": 0.692497166675351,
              "unit": "dimensionless"
            },
            {
              "label": "Liquid density",
              "value": 614.6517041106838,
              "unit": "kg/m3"
            },
            {
              "label": "Vapor density",
              "value": 11.765675360555246,
              "unit": "kg/m3"
            },
            {
              "label": "Maximum component balance error",
              "value": 5.551115123125783e-17,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum log-fugacity mismatch",
              "value": 5.403474265253116e-10,
              "unit": "dimensionless"
            },
            {
              "label": "Maximum relative EOS pressure residual",
              "value": 1.9207524459829983e-11,
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